
(/VERSIONCHECK 2) 

(DEFUN |FFNBP;coerce;GF$;1| (|v| $)
  (MAKEARR1 (QREFELT $ 17) (SPADCALL |v| (QREFELT $ 45) (QREFELT $ 50)))) 

(PUT '|FFNBP;represents;V$;2| '|SPADreplace| '(XLAM (|v|) |v|)) 

(DEFUN |FFNBP;represents;V$;2| (|v| $) |v|) 

(DEFUN |FFNBP;degree;$Pi;3| (|a| $)
  (PROG (|d| |b|)
    (RETURN
     (SEQ (LETT |d| 1 . #1=(|FFNBP;degree;$Pi;3|))
          (LETT |b| (SPADCALL |a| 1 (QREFELT $ 53)) . #1#)
          (SEQ G190 (COND ((NULL (SPADCALL |b| |a| (QREFELT $ 55))) (GO G191)))
               (SEQ (LETT |b| (SPADCALL |b| 1 (QREFELT $ 53)) . #1#)
                    (EXIT (LETT |d| (+ |d| 1) . #1#)))
               NIL (GO G190) G191 (EXIT NIL))
          (EXIT |d|))))) 

(DEFUN |FFNBP;linearAssociatedExp;$Sup$;4| (|x| |f| $)
  (PROG (|r| |xm|)
    (RETURN
     (SEQ
      (LETT |xm|
            (SPADCALL
             (SPADCALL (|spadConstant| $ 27) (QREFELT $ 17) (QREFELT $ 58))
             (|spadConstant| $ 21) (QREFELT $ 59))
            . #1=(|FFNBP;linearAssociatedExp;$Sup$;4|))
      (LETT |r|
            (SPADCALL
             (SPADCALL |f| (SPADCALL |x| (QREFELT $ 60)) (QREFELT $ 61)) |xm|
             (QREFELT $ 62))
            . #1#)
      (EXIT (SPADCALL |r| (QREFELT $ 17) (QREFELT $ 63))))))) 

(DEFUN |FFNBP;linearAssociatedLog;$Sup;5| (|x| $) (SPADCALL |x| (QREFELT $ 60))) 

(DEFUN |FFNBP;linearAssociatedOrder;$Sup;6| (|x| $)
  (PROG (|xm|)
    (RETURN
     (SEQ
      (LETT |xm|
            (SPADCALL
             (SPADCALL (|spadConstant| $ 27) (QREFELT $ 17) (QREFELT $ 58))
             (|spadConstant| $ 21) (QREFELT $ 59))
            |FFNBP;linearAssociatedOrder;$Sup;6|)
      (EXIT
       (SPADCALL |xm|
                 (SPADCALL |xm| (SPADCALL |x| (QREFELT $ 60)) (QREFELT $ 66))
                 (QREFELT $ 67))))))) 

(DEFUN |FFNBP;linearAssociatedLog;2$U;7| (|b| |x| $)
  (PROG (|e1| #1=#:G1850 |e| |xm|)
    (RETURN
     (SEQ
      (COND ((SPADCALL |x| (QREFELT $ 69)) (CONS 0 (|spadConstant| $ 19)))
            (#2='T
             (SEQ
              (LETT |xm|
                    (SPADCALL
                     (SPADCALL (|spadConstant| $ 27) (QREFELT $ 17)
                               (QREFELT $ 58))
                     (|spadConstant| $ 21) (QREFELT $ 59))
                    . #3=(|FFNBP;linearAssociatedLog;2$U;7|))
              (LETT |e|
                    (SPADCALL (SPADCALL |b| (QREFELT $ 60)) |xm|
                              (SPADCALL |x| (QREFELT $ 60)) (QREFELT $ 72))
                    . #3#)
              (EXIT
               (COND
                ((SPADCALL |e| (CONS 1 "failed") (QREFELT $ 75))
                 (CONS 1 "failed"))
                (#2#
                 (SEQ
                  (LETT |e1|
                        (PROG2
                            (LETT #1# |e| . #3#)
                            (QCDR #1#)
                          (|check-union| (QEQCAR #1# 0)
                                         (|Record|
                                          (|:| |coef1|
                                               (|SparseUnivariatePolynomial|
                                                (QREFELT $ 6)))
                                          (|:| |coef2|
                                               (|SparseUnivariatePolynomial|
                                                (QREFELT $ 6))))
                                         #1#))
                        . #3#)
                  (EXIT (CONS 0 (QCAR |e1|)))))))))))))) 

(DEFUN |FFNBP;getMultiplicationTable;V;8| ($)
  (SEQ (COND ((QREFELT $ 16) (|FFNBP;initializeMult| $)))
       (EXIT (QREFELT $ 23)))) 

(DEFUN |FFNBP;getMultiplicationMatrix;M;9| ($)
  (SEQ (COND ((QREFELT $ 16) (|FFNBP;initializeMult| $)))
       (EXIT (SPADCALL (QREFELT $ 23) (QREFELT $ 81))))) 

(DEFUN |FFNBP;sizeMultiplication;Nni;10| ($)
  (SEQ (COND ((QREFELT $ 16) (|FFNBP;initializeMult| $)))
       (EXIT (SPADCALL (QREFELT $ 23) (QREFELT $ 83))))) 

(DEFUN |FFNBP;trace;$GF;11| (|a| $)
  (SPADCALL (SPADCALL |a| 1 (QREFELT $ 85)) (QREFELT $ 86))) 

(DEFUN |FFNBP;norm;$GF;12| (|a| $)
  (SPADCALL (SPADCALL |a| 1 (QREFELT $ 88)) (QREFELT $ 86))) 

(DEFUN |FFNBP;generator;$;13| ($) (SPADCALL (QREFELT $ 17) (QREFELT $ 90))) 

(DEFUN |FFNBP;basis;PiV;14| (|n| $)
  (PROG (#1=#:G1876 |i| #2=#:G1875)
    (RETURN
     (SEQ
      (COND
       ((SPADCALL (REMAINDER2 (QREFELT $ 17) |n|) 0 (QREFELT $ 92))
        (|error| "argument must divide extension degree"))
       ('T
        (PROGN
         (LETT #2# (GETREFV |n|) . #3=(|FFNBP;basis;PiV;14|))
         (SEQ (LETT |i| 0 . #3#) (LETT #1# (- |n| 1) . #3#) G190
              (COND ((QSGREATERP |i| #1#) (GO G191)))
              (SEQ
               (EXIT
                (SETELT #2# |i|
                        (SPADCALL
                         (SPADCALL (SPADCALL (QREFELT $ 93)) |n|
                                   (QREFELT $ 85))
                         |i| (QREFELT $ 94)))))
              (LETT |i| (QSADD1 |i|) . #3#) (GO G190) G191 (EXIT NIL))
         #2#))))))) 

(DEFUN |FFNBP;*;GF2$;15| (|a| |x| $) (SPADCALL |a| |x| (QREFELT $ 97))) 

(DEFUN |FFNBP;/;$GF$;16| (|x| |a| $)
  (SPADCALL |x| (SPADCALL |a| (QREFELT $ 51)) (QREFELT $ 99))) 

(PUT '|FFNBP;coordinates;$V;17| '|SPADreplace| '(XLAM (|x|) |x|)) 

(DEFUN |FFNBP;coordinates;$V;17| (|x| $) |x|) 

(DEFUN |FFNBP;Frobenius;2$;18| (|e| $) (SPADCALL |e| 1 (QREFELT $ 53))) 

(DEFUN |FFNBP;Frobenius;$Nni$;19| (|e| |n| $) (SPADCALL |e| |n| (QREFELT $ 53))) 

(DEFUN |FFNBP;retractIfCan;$U;20| (|x| $)
  (COND
   ((SPADCALL |x| (QREFELT $ 103))
    (CONS 0
          (SPADCALL (SPADCALL |x| 1 (QREFELT $ 104)) (QREFELT $ 45)
                    (QREFELT $ 105))))
   ('T (CONS 1 "failed")))) 

(DEFUN |FFNBP;retract;$GF;21| (|x| $)
  (COND
   ((SPADCALL |x| (QREFELT $ 103))
    (SPADCALL (SPADCALL |x| 1 (QREFELT $ 104)) (QREFELT $ 45) (QREFELT $ 105)))
   ('T (|error| "element not in ground field")))) 

(DEFUN |FFNBP;coerce;$Of;22| (|x| $)
  (PROG (|r| |l| |mon| |i| #1=#:G1902 |b| |n|)
    (RETURN
     (SEQ (LETT |l| NIL . #2=(|FFNBP;coerce;$Of;22|))
          (LETT |n| (QREFELT $ 17) . #2#)
          (EXIT
           (COND
            ((EQL |n| 1)
             (SPADCALL (SPADCALL |x| 1 (QREFELT $ 104)) (QREFELT $ 108)))
            (#3='T
             (SEQ
              (SEQ (LETT |b| NIL . #2#) (LETT #1# (QREFELT $ 41) . #2#)
                   (LETT |i| 1 . #2#) G190
                   (COND
                    ((OR (QSGREATERP |i| |n|) (ATOM #1#)
                         (PROGN (LETT |b| (CAR #1#) . #2#) NIL))
                     (GO G191)))
                   (SEQ
                    (EXIT
                     (COND
                      ((NULL
                        (SPADCALL (SPADCALL |x| |i| (QREFELT $ 104))
                                  (QREFELT $ 109)))
                       (SEQ
                        (LETT |mon|
                              (COND
                               ((SPADCALL (SPADCALL |x| |i| (QREFELT $ 104))
                                          (|spadConstant| $ 27)
                                          (QREFELT $ 110))
                                |b|)
                               ('T
                                (SPADCALL
                                 (SPADCALL (SPADCALL |x| |i| (QREFELT $ 104))
                                           (QREFELT $ 108))
                                 |b| (QREFELT $ 111))))
                              . #2#)
                        (EXIT (LETT |l| (CONS |mon| |l|) . #2#)))))))
                   (LETT |i| (PROG1 (QSADD1 |i|) (LETT #1# (CDR #1#) . #2#))
                         . #2#)
                   (GO G190) G191 (EXIT NIL))
              (EXIT
               (COND
                ((NULL |l|) (SPADCALL (|spadConstant| $ 19) (QREFELT $ 114)))
                (#3#
                 (SEQ
                  (LETT |r| (SPADCALL (ELT $ 115) |l| (QREFELT $ 118)) . #2#)
                  (EXIT |r|))))))))))))) 

(DEFUN |FFNBP;initializeElt| ($)
  (SEQ
   (SETELT $ 42
           (SPADCALL
            (SPADCALL
             (-
              (SPADCALL (SPADCALL (QREFELT $ 120)) (QREFELT $ 17)
                        (QREFELT $ 121))
              1)
             (QREFELT $ 123))
            (QREFELT $ 127)))
   (SETELT $ 46 (SPADCALL (SPADCALL (QREFELT $ 128)) (QREFELT $ 129)))
   (SETELT $ 15 'NIL) (EXIT (SPADCALL (QREFELT $ 130))))) 

(DEFUN |FFNBP;initializeMult| ($)
  (SEQ (SETELT $ 23 (SPADCALL (QREFELT $ 20) (QREFELT $ 131)))
       (SPADCALL (QREFELT $ 23) (QREFELT $ 45) (QREFELT $ 34))
       (SETELT $ 16 'NIL) (EXIT (SPADCALL (QREFELT $ 130))))) 

(DEFUN |FFNBP;initializeLog| ($)
  (PROG (#1=#:G1924 |a| #2=#:G1930 #3=#:G1918 |i| |tbl| |n| |d| |l| |base|
         |fac| #4=#:G1929 |f| |limit|)
    (RETURN
     (SEQ (COND ((QREFELT $ 15) (|FFNBP;initializeElt| $)))
          (LETT |limit| 30 . #5=(|FFNBP;initializeLog|))
          (SEQ (LETT |f| NIL . #5#) (LETT #4# (QREFELT $ 42) . #5#) G190
               (COND
                ((OR (ATOM #4#) (PROGN (LETT |f| (CAR #4#) . #5#) NIL))
                 (GO G191)))
               (SEQ (LETT |fac| (QCAR |f|) . #5#)
                    (LETT |base|
                          (SPADCALL (SPADCALL (QREFELT $ 46) (QREFELT $ 132))
                                    (QUOTIENT2
                                     (-
                                      (SPADCALL (SPADCALL (QREFELT $ 120))
                                                (QREFELT $ 17) (QREFELT $ 121))
                                      1)
                                     |fac|)
                                    (QREFELT $ 133))
                          . #5#)
                    (LETT |l| (INTEGER-LENGTH |fac|) . #5#) (LETT |n| 0 . #5#)
                    (COND
                     ((ODDP |l|)
                      (LETT |n| (ASH |fac| (- (QUOTIENT2 |l| 2))) . #5#))
                     ('T (LETT |n| (ASH 1 (QUOTIENT2 |l| 2)) . #5#)))
                    (COND
                     ((< |n| |limit|)
                      (SEQ
                       (LETT |d| (+ (QUOTIENT2 (- |fac| 1) |limit|) 1) . #5#)
                       (EXIT
                        (LETT |n| (+ (QUOTIENT2 (- |fac| 1) |d|) 1) . #5#)))))
                    (LETT |tbl| (SPADCALL (QREFELT $ 135)) . #5#)
                    (LETT |a| (|spadConstant| $ 22) . #5#)
                    (SEQ (LETT |i| 0 . #5#)
                         (LETT #2#
                               (PROG1 (LETT #3# (- |n| 1) . #5#)
                                 (|check-subtype| (>= #3# 0)
                                                  '(|NonNegativeInteger|) #3#))
                               . #5#)
                         G190 (COND ((QSGREATERP |i| #2#) (GO G191)))
                         (SEQ
                          (SPADCALL (CONS (SPADCALL |a| (QREFELT $ 129)) |i|)
                                    |tbl| (QREFELT $ 137))
                          (EXIT
                           (LETT |a| (SPADCALL |a| |base| (QREFELT $ 138))
                                 . #5#)))
                         (LETT |i| (QSADD1 |i|) . #5#) (GO G190) G191
                         (EXIT NIL))
                    (EXIT
                     (SPADCALL
                      (CONS
                       (PROG1 (LETT #1# |fac| . #5#)
                         (|check-subtype| (> #1# 0) '(|PositiveInteger|) #1#))
                       (SPADCALL |tbl| (QREFELT $ 139)))
                      (QREFELT $ 49) (QREFELT $ 141))))
               (LETT #4# (CDR #4#) . #5#) (GO G190) G191 (EXIT NIL))
          (SETELT $ 14 'NIL) (EXIT (SPADCALL (QREFELT $ 130))))))) 

(DEFUN |FFNBP;tableForDiscreteLogarithm;IT;26| (|fac| $)
  (PROG (|tbl| #1=#:G1932)
    (RETURN
     (SEQ (COND ((QREFELT $ 14) (|FFNBP;initializeLog| $)))
          (LETT |tbl|
                (SPADCALL
                 (PROG1
                     (LETT #1# |fac|
                           . #2=(|FFNBP;tableForDiscreteLogarithm;IT;26|))
                   (|check-subtype| (> #1# 0) '(|PositiveInteger|) #1#))
                 (QREFELT $ 49) (QREFELT $ 143))
                . #2#)
          (EXIT
           (COND
            ((QEQCAR |tbl| 1)
             (|error|
              "tableForDiscreteLogarithm: argument must be prime divisor of the order of the multiplicative group"))
            ('T (QCDR |tbl|)))))))) 

(DEFUN |FFNBP;primitiveElement;$;27| ($)
  (SEQ (COND ((QREFELT $ 15) (|FFNBP;initializeElt| $)))
       (EXIT (SPADCALL (QREFELT $ 46) (QREFELT $ 132))))) 

(DEFUN |FFNBP;factorsOfCyclicGroupSize;L;28| ($)
  (SEQ (COND ((NULL (QREFELT $ 42)) (|FFNBP;initializeElt| $)))
       (EXIT (QREFELT $ 42)))) 

(DEFUN |FFNBP;extensionDegree;Pi;29| ($) (QREFELT $ 17)) 

(DEFUN |FFNBP;definingPolynomial;Sup;30| ($) (QREFELT $ 20)) 

(DEFUN |FFNBP;trace;$Pi$;31| (|a| |d| $)
  (PROG (|erg| #1=#:G1948 |i| |v|)
    (RETURN
     (SEQ
      (LETT |v| (SPADCALL |a| |d| (QREFELT $ 149))
            . #2=(|FFNBP;trace;$Pi$;31|))
      (LETT |erg| |v| . #2#)
      (SEQ (LETT |i| 2 . #2#) (LETT #1# (QUOTIENT2 (QREFELT $ 17) |d|) . #2#)
           G190 (COND ((QSGREATERP |i| #1#) (GO G191)))
           (SEQ (EXIT (LETT |erg| (SPADCALL |erg| |v| (QREFELT $ 150)) . #2#)))
           (LETT |i| (QSADD1 |i|) . #2#) (GO G190) G191 (EXIT NIL))
      (EXIT |erg|))))) 

(DEFUN |FFNBP;characteristic;Nni;32| ($) (SPADCALL (QREFELT $ 151))) 

(DEFUN |FFNBP;random;$;33| ($) (SPADCALL (QREFELT $ 17) (QREFELT $ 153))) 

(DEFUN |FFNBP;*;3$;34| (|x| |y| $)
  (SEQ (COND ((QREFELT $ 16) (|FFNBP;initializeMult| $)))
       (SPADCALL (QREFELT $ 23) (QREFELT $ 45) (QREFELT $ 34))
       (EXIT (SPADCALL |x| |y| (QREFELT $ 155))))) 

(DEFUN |FFNBP;One;$;35| ($)
  (MAKEARR1 (QREFELT $ 17) (SPADCALL (QREFELT $ 45) (QREFELT $ 156)))) 

(DEFUN |FFNBP;Zero;$;36| ($) (SPADCALL (QREFELT $ 17) (QREFELT $ 157))) 

(DEFUN |FFNBP;size;Nni;37| ($)
  (SPADCALL (SPADCALL (QREFELT $ 120)) (QREFELT $ 17) (QREFELT $ 121))) 

(DEFUN |FFNBP;index;Pi$;38| (|n| $)
  (SPADCALL (QREFELT $ 17) |n| (QREFELT $ 159))) 

(DEFUN |FFNBP;lookup;$Pi;39| (|x| $) (SPADCALL |x| (QREFELT $ 160))) 

(DEFUN |FFNBP;basis;V;40| ($)
  (PROG (#1=#:G1962 |e| #2=#:G1961 |a|)
    (RETURN
     (SEQ
      (LETT |a| (SPADCALL (QREFELT $ 17) (QREFELT $ 162))
            . #3=(|FFNBP;basis;V;40|))
      (EXIT
       (SPADCALL
        (PROGN
         (LETT #2# NIL . #3#)
         (SEQ (LETT |e| NIL . #3#)
              (LETT #1# (SPADCALL |a| (QREFELT $ 164)) . #3#) G190
              (COND
               ((OR (ATOM #1#) (PROGN (LETT |e| (CAR #1#) . #3#) NIL))
                (GO G191)))
              (SEQ (EXIT (LETT #2# (CONS |e| #2#) . #3#)))
              (LETT #1# (CDR #1#) . #3#) (GO G190) G191 (EXIT (NREVERSE #2#))))
        (QREFELT $ 167))))))) 

(DEFUN |FFNBP;^;$I$;41| (|x| |e| $)
  (SEQ (COND ((QREFELT $ 16) (|FFNBP;initializeMult| $)))
       (SPADCALL (QREFELT $ 23) (QREFELT $ 45) (QREFELT $ 34))
       (EXIT (SPADCALL |x| |e| (QREFELT $ 169))))) 

(DEFUN |FFNBP;normal?;$B;42| (|x| $) (SPADCALL |x| (QREFELT $ 170))) 

(DEFUN |FFNBP;-;2$;43| (|x| $) (SPADCALL |x| (QREFELT $ 172))) 

(DEFUN |FFNBP;+;3$;44| (|x| |y| $) (SPADCALL |x| |y| (QREFELT $ 174))) 

(DEFUN |FFNBP;-;3$;45| (|x| |y| $) (SPADCALL |x| |y| (QREFELT $ 176))) 

(DEFUN |FFNBP;=;2$B;46| (|x| |y| $) (SPADCALL |x| |y| (QREFELT $ 178))) 

(DEFUN |FFNBP;*;I2$;47| (|n| |x| $)
  (SPADCALL |x| (SPADCALL |n| (QREFELT $ 180)) (QREFELT $ 181))) 

(PUT '|FFNBP;representationType;U;48| '|SPADreplace|
     '(XLAM NIL (CONS 2 "normal"))) 

(DEFUN |FFNBP;representationType;U;48| ($) (CONS 2 "normal")) 

(DEFUN |FFNBP;minimalPolynomial;$Sup;49| (|a| $)
  (SEQ (COND ((QREFELT $ 16) (|FFNBP;initializeMult| $)))
       (SPADCALL (QREFELT $ 23) (QREFELT $ 45) (QREFELT $ 34))
       (EXIT (SPADCALL |a| (QREFELT $ 36))))) 

(DEFUN |FFNBP;inGroundField?;$B;50| (|x| $)
  (PROG (#1=#:G1985 |erg| #2=#:G1988 |i|)
    (RETURN
     (SEQ (LETT |erg| 'T . #3=(|FFNBP;inGroundField?;$B;50|))
          (SEQ
           (EXIT
            (SEQ (LETT |i| 2 . #3#) (LETT #2# (QREFELT $ 17) . #3#) G190
                 (COND ((QSGREATERP |i| #2#) (GO G191)))
                 (SEQ
                  (EXIT
                   (COND
                    ((NULL
                      (SPADCALL (SPADCALL |x| |i| (QREFELT $ 104))
                                (SPADCALL |x| 1 (QREFELT $ 104))
                                (QREFELT $ 110)))
                     (PROGN
                      (LETT #1# (LETT |erg| 'NIL . #3#) . #3#)
                      (GO #1#))))))
                 (LETT |i| (QSADD1 |i|) . #3#) (GO G190) G191 (EXIT NIL)))
           #1# (EXIT #1#))
          (EXIT |erg|))))) 

(DEFUN |FFNBP;/;3$;51| (|x| |y| $)
  (SEQ (COND ((QREFELT $ 16) (|FFNBP;initializeMult| $)))
       (SPADCALL (QREFELT $ 23) (QREFELT $ 45) (QREFELT $ 34))
       (EXIT (SPADCALL |x| |y| (QREFELT $ 186))))) 

(DEFUN |FFNBP;inv;2$;52| (|a| $)
  (SEQ (COND ((QREFELT $ 16) (|FFNBP;initializeMult| $)))
       (SPADCALL (QREFELT $ 23) (QREFELT $ 45) (QREFELT $ 34))
       (EXIT (SPADCALL |a| (QREFELT $ 187))))) 

(DEFUN |FFNBP;norm;$Pi$;53| (|a| |d| $)
  (SEQ (COND ((QREFELT $ 16) (|FFNBP;initializeMult| $)))
       (SPADCALL (QREFELT $ 23) (QREFELT $ 45) (QREFELT $ 34))
       (EXIT (SPADCALL |a| |d| (QREFELT $ 189))))) 

(DEFUN |FFNBP;normalElement;$;54| ($) (SPADCALL (QREFELT $ 17) (QREFELT $ 90))) 

(DEFUN |FiniteFieldNormalBasisExtensionByPolynomial| (&REST #1=#:G2016)
  (PROG ()
    (RETURN
     (PROG (#2=#:G2017)
       (RETURN
        (COND
         ((LETT #2#
                (|lassocShiftWithFunction| (|devaluateList| #1#)
                                           (HGET |$ConstructorCache|
                                                 '|FiniteFieldNormalBasisExtensionByPolynomial|)
                                           '|domainEqualList|)
                . #3=(|FiniteFieldNormalBasisExtensionByPolynomial|))
          (|CDRwithIncrement| #2#))
         ('T
          (UNWIND-PROTECT
              (PROG1
                  (APPLY
                   (|function| |FiniteFieldNormalBasisExtensionByPolynomial;|)
                   #1#)
                (LETT #2# T . #3#))
            (COND
             ((NOT #2#)
              (HREM |$ConstructorCache|
                    '|FiniteFieldNormalBasisExtensionByPolynomial|))))))))))) 

(DEFUN |FiniteFieldNormalBasisExtensionByPolynomial;| (|#1| |#2|)
  (PROG (#1=#:G1830 #2=#:G2015 |i| #3=#:G2014 |qs| |pv$| #4=#:G2013 $ |dv$|
         DV$2 DV$1)
    (RETURN
     (SEQ
      (PROGN
       (LETT DV$1 (|devaluate| |#1|)
             . #5=(|FiniteFieldNormalBasisExtensionByPolynomial|))
       (LETT DV$2 (|devaluate| |#2|) . #5#)
       (LETT |dv$|
             (LIST '|FiniteFieldNormalBasisExtensionByPolynomial| DV$1 DV$2)
             . #5#)
       (LETT $ (GETREFV 207) . #5#)
       (QSETREFV $ 0 |dv$|)
       (QSETREFV $ 3
                 (LETT |pv$|
                       (|buildPredVector| 0 0
                                          (LIST
                                           (|HasCategory| |#1|
                                                          '(|CharacteristicZero|))
                                           (LETT #4#
                                                 (|HasCategory| |#1|
                                                                '(|Finite|))
                                                 . #5#)
                                           (OR
                                            (|HasCategory| |#1|
                                                           '(|CharacteristicNonZero|))
                                            #4#)))
                       . #5#))
       (|haddProp| |$ConstructorCache|
                   '|FiniteFieldNormalBasisExtensionByPolynomial|
                   (LIST DV$1 DV$2) (CONS 1 $))
       (|stuffDomainSlots| $)
       (QSETREFV $ 6 |#1|)
       (QSETREFV $ 7 |#2|)
       (SETF |pv$| (QREFELT $ 3))
       (QSETREFV $ 8 (|Vector| |#1|))
       (QSETREFV $ 13 (SPADCALL (SPADCALL (QREFELT $ 10)) (QREFELT $ 12)))
       (QSETREFV $ 14 'T)
       (QSETREFV $ 15 'T)
       (QSETREFV $ 16 'T)
       (QSETREFV $ 17 1)
       (QSETREFV $ 20 (|spadConstant| $ 19))
       (QSETREFV $ 23 (MAKEARR1 1 NIL))
       (COND
        ((QEQCAR |#2| 1)
         (PROGN
          (SETELT $ 23 (QCDR |#2|))
          (SETELT $ 17 (QVSIZE (QREFELT $ 23)))
          (QSETREFV $ 26 (MAKEARR1 (QREFELT $ 17) (|spadConstant| $ 25)))
          (SPADCALL (QREFELT $ 26) 1 (|spadConstant| $ 27) (QREFELT $ 29))
          (SPADCALL (QREFELT $ 23) (|spadConstant| $ 27) (QREFELT $ 34))
          (SETELT $ 20 (SPADCALL (QREFELT $ 26) (QREFELT $ 36)))
          (SETELT $ 16 'NIL)))
        ('T
         (PROGN
          (SETELT $ 20 (QCDR |#2|))
          (SETELT $ 17 (SPADCALL (QREFELT $ 20) (QREFELT $ 38)))
          (SETELT $ 23 (MAKEARR1 (QREFELT $ 17) NIL)))))
       (QSETREFV $ 41
                 (SEQ (LETT |qs| (SPADCALL '|q| (QREFELT $ 12)) . #5#)
                      (EXIT
                       (APPEND
                        (LIST (QREFELT $ 13)
                              (SPADCALL (QREFELT $ 13) |qs| (QREFELT $ 39)))
                        (PROGN
                         (LETT #3# NIL . #5#)
                         (SEQ (LETT |i| 2 . #5#)
                              (LETT #2# (- (QREFELT $ 17) 1) . #5#) G190
                              (COND ((QSGREATERP |i| #2#) (GO G191)))
                              (SEQ
                               (EXIT
                                (LETT #3#
                                      (CONS
                                       (SPADCALL (QREFELT $ 13)
                                                 (SPADCALL |qs|
                                                           (SPADCALL |i|
                                                                     (QREFELT $
                                                                              40))
                                                           (QREFELT $ 39))
                                                 (QREFELT $ 39))
                                       #3#)
                                      . #5#)))
                              (LETT |i| (QSADD1 |i|) . #5#) (GO G190) G191
                              (EXIT (NREVERSE #3#))))))))
       (QSETREFV $ 42 NIL)
       (QSETREFV $ 45
                 (SPADCALL
                  (SPADCALL (QREFELT $ 20)
                            (PROG1
                                (LETT #1#
                                      (-
                                       (SPADCALL (QREFELT $ 20) (QREFELT $ 38))
                                       1)
                                      . #5#)
                              (|check-subtype| (>= #1# 0)
                                               '(|NonNegativeInteger|) #1#))
                            (QREFELT $ 43))
                  (QREFELT $ 44)))
       (QSETREFV $ 46 1)
       (QSETREFV $ 49 (SPADCALL (QREFELT $ 48)))
       $))))) 

(MAKEPROP '|FiniteFieldNormalBasisExtensionByPolynomial| '|infovec|
          (LIST
           '#(NIL NIL NIL NIL NIL NIL (|local| |#1|) (|local| |#2|) '|Rep|
              (|Symbol|) (0 . |new|) (|OutputForm|) (4 . |coerce|) '|alpha|
              '|initlog?| '|initelt?| '|initmult?| '|extdeg|
              (|SparseUnivariatePolynomial| 6) (9 . |Zero|) '|defpol|
              (13 . |One|)
              (CONS IDENTITY (FUNCALL (|dispatchFunction| |FFNBP;One;$;35|) $))
              '|multTable|
              (CONS IDENTITY
                    (FUNCALL (|dispatchFunction| |FFNBP;Zero;$;36|) $))
              (17 . |Zero|) '|vv| (21 . |One|) (|Integer|) (25 . |setelt|)
              (|Void|) (|Record| (|:| |value| 6) (|:| |index| 206))
              (|Vector| (|List| 31)) (|InnerNormalBasisFieldFunctions| 6)
              (32 . |setFieldInfo|) (|Vector| 6) (38 . |minimalPolynomial|)
              (|NonNegativeInteger|) (43 . |degree|) (48 . ^) (54 . |coerce|)
              '|basisOutput| '|facOfGroupSize| (59 . |coefficient|) (65 . -)
              '|traceAlpha| '|primitiveElt| (|Table| 56 134) (70 . |table|)
              '|discLogTable| (74 . /) |FFNBP;coerce;GF$;1|
              |FFNBP;represents;V$;2| (80 . |qPot|) (|Boolean|) (86 . ~=)
              (|PositiveInteger|) |FFNBP;degree;$Pi;3| (92 . |monomial|)
              (98 . -) (104 . |pol|) (109 . *) (115 . |rem|)
              (121 . |vectorise|) |FFNBP;linearAssociatedExp;$Sup$;4|
              |FFNBP;linearAssociatedLog;$Sup;5| (127 . |gcd|) (133 . |quo|)
              |FFNBP;linearAssociatedOrder;$Sup;6| (139 . |zero?|)
              (|Record| (|:| |coef1| $) (|:| |coef2| $))
              (|Union| 70 '#1="failed") (144 . |extendedEuclidean|)
              (|Record| (|:| |coef1| 18) (|:| |coef2| 18)) (|Union| 73 '#1#)
              (151 . =) (|Union| 18 '"failed")
              |FFNBP;linearAssociatedLog;2$U;7|
              |FFNBP;getMultiplicationTable;V;8| (|Matrix| 6)
              (|FiniteFieldFunctions| 6) (157 . |createMultiplicationMatrix|)
              |FFNBP;getMultiplicationMatrix;M;9| (162 . |sizeMultiplication|)
              |FFNBP;sizeMultiplication;Nni;10| |FFNBP;trace;$Pi$;31|
              |FFNBP;retract;$GF;21| |FFNBP;trace;$GF;11| |FFNBP;norm;$Pi$;53|
              |FFNBP;norm;$GF;12| (167 . |normalElement|)
              |FFNBP;generator;$;13| (172 . ~=) |FFNBP;normalElement;$;54|
              |FFNBP;Frobenius;$Nni$;19| (|Vector| $) |FFNBP;basis;PiV;14|
              (178 . *) |FFNBP;*;GF2$;15| |FFNBP;/;3$;51| |FFNBP;/;$GF$;16|
              |FFNBP;coordinates;$V;17| |FFNBP;Frobenius;2$;18|
              |FFNBP;inGroundField?;$B;50| (184 . |elt|) (190 . *)
              (|Union| 6 '"failed") |FFNBP;retractIfCan;$U;20| (196 . |coerce|)
              (201 . |zero?|) (206 . =) (212 . *) (|Fraction| 18)
              (218 . |Zero|) (222 . |coerce|) (227 . +) (|Mapping| 11 11 11)
              (|List| 11) (233 . |reduce|) |FFNBP;coerce;$Of;22| (239 . |size|)
              (243 . ^) (|Factored| $) (249 . |factor|)
              (|Record| (|:| |factor| 28) (|:| |exponent| 28)) (|List| 124)
              (|Factored| 28) (254 . |factors|)
              (259 . |createPrimitiveElement|) |FFNBP;lookup;$Pi;39|
              (263 . |void|) (267 . |createMultiplicationTable|)
              |FFNBP;index;Pi$;38| |FFNBP;^;$I$;41| (|Table| 56 37)
              (272 . |table|) (|Record| (|:| |key| 56) (|:| |entry| 37))
              (276 . |insert!|) |FFNBP;*;3$;34| (282 . |copy|)
              (|Record| (|:| |key| 56) (|:| |entry| 134)) (287 . |insert!|)
              (|Union| 134 '"failed") (293 . |search|)
              |FFNBP;tableForDiscreteLogarithm;IT;26|
              |FFNBP;primitiveElement;$;27|
              |FFNBP;factorsOfCyclicGroupSize;L;28|
              |FFNBP;extensionDegree;Pi;29| |FFNBP;definingPolynomial;Sup;30|
              (299 . |trace|) (305 . |concat|) (311 . |characteristic|)
              |FFNBP;characteristic;Nni;32| (315 . |random|)
              |FFNBP;random;$;33| (320 . *) (326 . |inv|) (331 . |zero|)
              |FFNBP;size;Nni;37| (336 . |index|) (342 . |lookup|)
              (|Vector| 35) (347 . |basis|) (|List| 35) (352 . |entries|)
              (|List| $$) (|Vector| $$) (357 . |vector|) |FFNBP;basis;V;40|
              (362 . ^) (368 . |normal?|) |FFNBP;normal?;$B;42| (373 . -)
              |FFNBP;-;2$;43| (378 . +) |FFNBP;+;3$;44| (384 . -)
              |FFNBP;-;3$;45| (390 . =) |FFNBP;=;2$B;46| (396 . |coerce|)
              (401 . *) |FFNBP;*;I2$;47|
              (|Union| '"prime" '"polynomial" '"normal" '"cyclic")
              |FFNBP;representationType;U;48| |FFNBP;minimalPolynomial;$Sup;49|
              (407 . /) (413 . |inv|) |FFNBP;inv;2$;52| (418 . |norm|)
              (|OnePointCompletion| 56) (|Union| $ '"failed")
              (|Union| 37 '"failed") (|List| $) (|InputForm|)
              (|Union| 95 '"failed") (|Matrix| $)
              (|SparseUnivariatePolynomial| $) (|CardinalNumber|)
              (|Fraction| 28) (|Union| 193 '"failed")
              (|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $))
              (|Record| (|:| |quotient| $) (|:| |remainder| $))
              (|Record| (|:| |coef| 193) (|:| |generator| $))
              (|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $))
              (|String|) (|SingleInteger|))
           '#(~= 424 |zero?| 430 |unitNormal| 435 |unitCanonical| 440 |unit?|
              445 |transcendent?| 450 |transcendenceDegree| 455 |trace| 459
              |tableForDiscreteLogarithm| 470 |subtractIfCan| 475
              |squareFreePart| 481 |squareFree| 486 |sizeMultiplication| 491
              |sizeLess?| 495 |size| 501 |sample| 505 |retractIfCan| 509
              |retract| 514 |represents| 519 |representationType| 524 |rem| 528
              |recip| 534 |random| 539 |quo| 543 |principalIdeal| 549
              |primitiveElement| 554 |primitive?| 558 |primeFrobenius| 563
              |prime?| 574 |order| 579 |one?| 589 |normalElement| 594 |normal?|
              598 |norm| 603 |nextItem| 614 |multiEuclidean| 619
              |minimalPolynomial| 625 |lookup| 636 |linearAssociatedOrder| 641
              |linearAssociatedLog| 646 |linearAssociatedExp| 657 |lcm| 663
              |latex| 674 |inv| 679 |init| 684 |index| 688 |inGroundField?| 693
              |hash| 698 |getMultiplicationTable| 703 |getMultiplicationMatrix|
              707 |generator| 711 |gcdPolynomial| 715 |gcd| 721
              |factorsOfCyclicGroupSize| 732 |factor| 736 |extensionDegree| 741
              |extendedEuclidean| 749 |exquo| 762 |expressIdealMember| 768
              |euclideanSize| 774 |enumerate| 779 |divide| 783 |discreteLog|
              789 |dimension| 800 |differentiate| 804 |degree| 815
              |definingPolynomial| 825 |createPrimitiveElement| 829
              |createNormalElement| 833 |coordinates| 837 |convert| 847
              |conditionP| 852 |coerce| 857 |charthRoot| 882 |characteristic|
              892 |basis| 896 |associates?| 905 |algebraic?| 911 ^ 916 |Zero|
              934 |One| 938 |Frobenius| 942 D 953 = 964 / 970 - 982 + 993 *
              999)
           'NIL
           (CONS
            (|makeByteWordVec2| 3
                                '(0 0 2 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 2 0
                                  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0
                                  0 0 0 0 0 0 2))
            (CONS
             '#(|FiniteAlgebraicExtensionField&| |ExtensionField&|
                |FiniteFieldCategory&| |FieldOfPrimeCharacteristic&| |Field&|
                |EuclideanDomain&| NIL |UniqueFactorizationDomain&|
                |GcdDomain&| |DivisionRing&| |IntegralDomain&| |VectorSpace&|
                |Algebra&| |Algebra&| |Module&| |Module&| NIL NIL |Module&| NIL
                NIL |DifferentialRing&| NIL NIL NIL |Ring&| NIL NIL NIL NIL NIL
                NIL NIL |AbelianGroup&| NIL NIL |AbelianMonoid&| |Monoid&| NIL
                |SemiGroup&| |AbelianSemiGroup&| |Finite&| NIL |SetCategory&|
                |RetractableTo&| NIL NIL NIL NIL NIL |BasicType&| NIL NIL)
             (CONS
              '#((|FiniteAlgebraicExtensionField| 6) (|ExtensionField| 6)
                 (|FiniteFieldCategory|) (|FieldOfPrimeCharacteristic|)
                 (|Field|) (|EuclideanDomain|) (|PrincipalIdealDomain|)
                 (|UniqueFactorizationDomain|) (|GcdDomain|) (|DivisionRing|)
                 (|IntegralDomain|) (|VectorSpace| 6) (|Algebra| 199)
                 (|Algebra| $$) (|Module| 6) (|Module| 199) (|EntireRing|)
                 (|CommutativeRing|) (|Module| $$) (|CharacteristicNonZero|)
                 (|CharacteristicZero|) (|DifferentialRing|) (|BiModule| 6 6)
                 (|BiModule| 199 199) (|BiModule| $$ $$) (|Ring|)
                 (|RightModule| 6) (|LeftModule| 6) (|RightModule| 199)
                 (|LeftModule| 199) (|LeftModule| $$) (|Rng|)
                 (|RightModule| $$) (|AbelianGroup|)
                 (|CancellationAbelianMonoid|) (|SemiRing|) (|AbelianMonoid|)
                 (|Monoid|) (|SemiRng|) (|SemiGroup|) (|AbelianSemiGroup|)
                 (|Finite|) (|StepThrough|) (|SetCategory|) (|RetractableTo| 6)
                 (|canonicalsClosed|) (|canonicalUnitNormal|)
                 (|noZeroDivisors|) (|CommutativeStar|) (|unitsKnown|)
                 (|BasicType|) (|CoercibleTo| 11) (|ConvertibleTo| 194))
              (|makeByteWordVec2| 206
                                  '(0 9 0 10 1 9 11 0 12 0 18 0 19 0 18 0 21 0
                                    6 0 25 0 6 0 27 3 8 6 0 28 6 29 2 33 30 32
                                    6 34 1 33 18 35 36 1 18 37 0 38 2 11 0 0 0
                                    39 1 37 11 0 40 2 18 6 0 37 43 1 6 0 0 44 0
                                    47 0 48 2 6 0 0 0 50 2 33 35 35 28 53 2 0
                                    54 0 0 55 2 18 0 6 37 58 2 18 0 0 0 59 1 33
                                    18 35 60 2 18 0 0 0 61 2 18 0 0 0 62 2 18
                                    35 0 37 63 2 18 0 0 0 66 2 18 0 0 0 67 1 0
                                    54 0 69 3 18 71 0 0 0 72 2 74 54 0 0 75 1
                                    80 79 32 81 1 80 37 32 83 1 33 35 56 90 2
                                    37 54 0 0 92 2 8 0 6 0 97 2 8 6 0 28 104 2
                                    6 0 0 0 105 1 6 11 0 108 1 6 54 0 109 2 6
                                    54 0 0 110 2 11 0 0 0 111 0 112 0 113 1 18
                                    11 0 114 2 11 0 0 0 115 2 117 11 116 0 118
                                    0 6 37 120 2 37 0 0 56 121 1 28 122 0 123 1
                                    126 125 0 127 0 0 0 128 0 30 0 130 1 80 32
                                    18 131 0 134 0 135 2 134 0 136 0 137 1 134
                                    0 0 139 2 47 0 140 0 141 2 47 142 56 0 143
                                    2 33 35 35 56 149 2 8 0 0 0 150 0 6 37 151
                                    1 33 35 56 153 2 33 35 35 35 155 1 6 0 0
                                    156 1 8 0 37 157 2 33 35 56 56 159 1 33 56
                                    35 160 1 33 161 56 162 1 161 163 0 164 1
                                    166 0 165 167 2 33 35 35 28 169 1 33 54 35
                                    170 1 8 0 0 172 2 8 0 0 0 174 2 8 0 0 0 176
                                    2 8 54 0 0 178 1 6 0 28 180 2 8 0 0 6 181 2
                                    33 35 35 35 186 1 33 35 35 187 2 33 35 35
                                    56 189 2 0 54 0 0 55 1 0 54 0 69 1 0 204 0
                                    1 1 0 0 0 1 1 0 54 0 1 1 0 54 0 1 0 0 37 1
                                    2 2 0 0 56 85 1 0 6 0 87 1 2 134 28 144 2 0
                                    191 0 0 1 1 0 0 0 1 1 0 122 0 1 0 0 37 84 2
                                    0 54 0 0 1 0 2 37 158 0 0 0 1 1 0 106 0 107
                                    1 0 6 0 86 1 0 0 35 52 0 2 183 184 2 0 0 0
                                    0 1 1 0 191 0 1 0 2 0 154 2 0 0 0 0 1 1 0
                                    203 193 1 0 2 0 145 1 2 54 0 1 1 3 0 0 1 2
                                    3 0 0 37 1 1 0 54 0 1 1 3 190 0 1 1 2 56 0
                                    1 1 0 54 0 1 0 2 0 93 1 2 54 0 171 2 2 0 0
                                    56 88 1 0 6 0 89 1 2 191 0 1 2 0 200 193 0
                                    1 2 2 197 0 56 1 1 0 18 0 185 1 2 56 0 129
                                    1 2 18 0 68 2 2 76 0 0 77 1 2 18 0 65 2 2 0
                                    0 18 64 2 0 0 0 0 1 1 0 0 193 1 1 0 205 0 1
                                    1 0 0 0 188 0 2 0 1 1 2 0 56 132 1 0 54 0
                                    103 1 0 206 0 1 0 0 32 78 0 0 79 82 0 2 0
                                    91 2 0 197 197 197 1 1 0 0 193 1 2 0 0 0 0
                                    1 0 2 125 146 1 0 122 0 1 0 0 56 147 0 0
                                    190 1 2 0 201 0 0 1 3 0 71 0 0 0 1 2 0 191
                                    0 0 1 2 0 200 193 0 1 1 0 37 0 1 0 2 193 1
                                    2 0 202 0 0 1 2 3 192 0 0 1 1 2 37 0 1 0 0
                                    198 1 2 2 0 0 37 1 1 2 0 0 1 1 0 56 0 57 1
                                    0 190 0 1 0 0 18 148 0 2 0 128 0 2 0 1 1 0
                                    35 0 101 1 0 79 95 1 1 2 194 0 1 1 2 195
                                    196 1 1 0 0 6 51 1 0 0 199 1 1 0 0 28 1 1 0
                                    0 0 1 1 0 11 0 119 1 3 191 0 1 1 2 0 0 1 0
                                    0 37 152 0 0 95 168 1 0 95 56 96 2 0 54 0 0
                                    1 1 0 54 0 1 2 0 0 0 28 133 2 0 0 0 37 1 2
                                    0 0 0 56 1 0 0 0 24 0 0 0 22 1 2 0 0 102 2
                                    2 0 0 37 94 2 2 0 0 37 1 1 2 0 0 1 2 0 54 0
                                    0 179 2 0 0 0 6 100 2 0 0 0 0 99 1 0 0 0
                                    173 2 0 0 0 0 177 2 0 0 0 0 175 2 0 0 6 0
                                    98 2 0 0 0 6 1 2 0 0 0 199 1 2 0 0 199 0 1
                                    2 0 0 28 0 182 2 0 0 0 0 138 2 0 0 37 0 1 2
                                    0 0 56 0 1)))))
           '|lookupComplete|)) 
